基于共形几何代数的高光谱遥感影像降维与分类

项目名称： 基于共形几何代数的高光谱遥感影像降维与分类

项目编号： No.41201341

项目类型： 青年科学基金项目

立项/批准年度： 2013

项目学科： 地理学

项目作者： 苏红军

作者单位： 河海大学

项目金额： 25万元

中文摘要： 共形几何代数具有统一几何表示、简洁代数形式和高效几何计算等特点，以共形几何代数为核心的新型理论框架和几何计算技术，为高光谱遥感影像的降维与分类研究提供了新的数学工具。本课题拟在共形几何代数与模式识别理论的基础上，研究基于共形几何代数的高光谱遥感影像的高效降维与高可信分类新方法。以实现更简洁、快速、鲁棒的高光谱遥感影像降维为切入点，研究基于共形几何代数的高维空间非线性信息表达模型、共形空间中高光谱影像信息描述模型；借鉴高维空间几何分析方法的优势，研究共形空间中基于共形几何代数的高光谱影像非线性特征提取方法；研究样本点在高维空间中的分布特征，构建基于共形几何代数的超球体分类器，实现小样本情况下高光谱遥感影像的高可信分类。本课题成果有望为高光谱遥感影像分析方法新增基础理论，推动高光谱遥感理论与技术的发展，促进高光谱遥感应用的深入。

中文关键词： 高光谱遥感；特征提取；特征选择；图像分类；共形几何代数

英文摘要： Conformal Geometric Algebra (CGA) has several advantages such as consistent geometric representation, compact algebra formulae, efficient geometric computing, coordinate free, and dimension independent etc., the new theoretical framework and geometric computing technology based on CGA provides a new mathematical tool for dimensionality reduction and classification of hyperspectral imagery. In this project, the efficient dimensionality reduction and high-reliable classification approaches for hyperspectral remotely sensed imagery based on CGA and pattern recognition technology are proposed. In order to achieve a more concise, fast, robust hyperspectral imagery dimensionality reduction, the non-linear information representation model in high-dimensional space and the information description model for hyperspectral imagery in conformal space based on CGA are put forward. Learned from the advantages of the geometric analysis in high-dimensional space, the CGA-supported nonlinear feature extraction methods in conformal space for hyperspectral imagery are designed. For high-reliable classification of hyperspectral images in the case of small number of samples, the distribution characteristics of the ground truth samples in high dimensional space will be studied, and then the hypersphere classifier with SVM based on th

英文关键词： Hyperspectral remote sensing；feature extraction；feature selection；imagery classification；conformal geometric algebra